On the other hand, the standard FA modelling of the inter-item tetrachoric correlation
matrix is equivalent to fitting the 2-parameter normalogive IRT model, while the FA modelling of the polychoric matrix is equivalent to fitting the normal-ogive version of Samejima's graded-response model (see e.g., Ferrando & Lorenzo-Seva, 2013, 2014; Mislevy, 1986; or Reckase, 2009).
After the scale has been set in two main categories, a Principal Component Analysis was performed based on the CCT assumptions, using the tetrachoric correlation
among the items of BISOC.
In addition, biserial correlation was used to study the relationship between the images and [L.sup.*], [a.sup.*], and [b.sup.*], and the I had used tetrachoric correlation
analysis to assess the relationship between the images and grain patterns.
Correlations between adherence measures were generally low (tetrachoric correlation
< = 0.20).
The simplest and oldest procedure, which Bock and Lieberman (1971) called the heuristic approach, consists of fitting the interitem tetrachoric correlation
matrix using the centroid method of FA (Lawley, 1955).
is a special case of analysis of the statistical covariation between two variables measured on a dichotomous scale, but assuming an underlying bivariate normal distribution.
In accordance with Bernstein and Teng (1989) and Panter, Swygert, Dahlstrom, and Tanaka (1997), to improve the factorial structure of the instrument while seeking to maintain its reliability, we decided to: a) reduce the number of items in the scale (by eliminating those items with item-total correlations inferior to 0.30, those with elevated dispersion in the response, and those with a percentage of nonresponse above 50%); and b) work with tetrachoric correlation
matrices instead of Pearson correlation matrices.
As a final note, the current factor analysis is run on the tetrachoric correlation
matrix because all variables are dichotomous.
To determine whether the responses to the reading items were consistent with unidimensionality, four different methods were applied: (1) principal component analysis of phi and tetrachoric correlation
matrices; (2) principal component analysis of the image correlation matrix, a method based on the work of Guttman; (3) R.
For this we performed the factor analysis for complete information, with oblique rotation, through the Microfact program using the IRT and tetrachoric correlation
coefficients, as they are suitable for items with dichotomous responses (Primi & Almeida, 1998).
Since binary items violate the basic assumption of a normal distribution, we used tetrachoric correlations
between the five e-MAPS items.